T he S tandard P uzzle C onstructing the model E xplaining the semantics Q uestion dependency H ow the D eontic I ssue in the M iners ’ P uzzle D epends on an E pistemic I ssue Martin Aher 1 Jeroen Groenendijk 2 1 Institute of Estonian and General Linguistics University of Tartu 2 Institute for Logic, Language and Computation University of Amsterdam Presented at SPE8 in Cambridge, 19.09.2015 Also presented at the Estonian-Finnish Logic Meeting in Rakvere, 15.11.2015 https://www.illc.uva.nl/inquisitivesemantics/
T he S tandard P uzzle C onstructing the model E xplaining the semantics Q uestion dependency T he S tory K olodny and M ac F arlane (2010) T he facts Miners are in one of two mine shafts. ∨ We can block either shaft. ∨ ∨ Blocking the correct mine shaft saves all miners. Blocking the wrong mine shaft kills all miners. Blocking neither mine shaft kills one miner. illclogo . pdf D eontic question (1) Ought shaft A, shaft B, or neither be blocked? ?( v p ′ ∨ v q ′ ∨ ( v ¬ p ′ ∧ v ¬ q ′ )) Notation: v , v are deontic, � , � epistemic modalities.
T he S tandard P uzzle C onstructing the model E xplaining the semantics Q uestion dependency T he S tory K olodny and M ac F arlane (2010) T he facts Miners are in one of two mine shafts. ∨ We can block either shaft. ∨ ∨ Blocking the correct mine shaft saves all miners. Blocking the wrong mine shaft kills all miners. Blocking neither mine shaft kills one miner. illclogo . pdf D eontic question (1) Ought shaft A, shaft B, or neither be blocked? ?( v p ′ ∨ v q ′ ∨ ( v ¬ p ′ ∧ v ¬ q ′ )) Notation: v , v are deontic, � , � epistemic modalities.
T he S tandard P uzzle C onstructing the model E xplaining the semantics Q uestion dependency T he S tory O ntic situation Dead Shafts Blocked None Some All All illclogo . pdf Some None
T he S tandard P uzzle C onstructing the model E xplaining the semantics Q uestion dependency T he S tory O ntic situation Dead Shafts Blocked None Some All All illclogo . pdf Some None
T he S tandard P uzzle C onstructing the model E xplaining the semantics Q uestion dependency T he S tory D eontic situation A im : least dead Dead Shafts Blocked None Some All illclogo . pdf All Some None Either shaft A or shaft B ought to be blocked. v p ′ ∨ v q ′ (2)
T he S tandard P uzzle C onstructing the model E xplaining the semantics Q uestion dependency T he S tory T he puzzle (3) a. The miners are in shaft A or shaft B. p ∨ q b. If the miners are in shaft A, we ought to block it. p → v p ′ c. If the miners are in shaft B, we ought to block it. q → v q ′ illclogo . pdf d. Hence, either shaft A or shaft B ought to be blocked. v p ′ ∨ v q ′
T he S tandard P uzzle C onstructing the model E xplaining the semantics Q uestion dependency T he S tory C onsider the information of the rescuers A im : least dead Dead Shafts Blocked None Some All Might kill all miners All illclogo . pdf Some None Either shaft ought to be blocked. v p ′ ∨ v q ′ (4) Intuition: neither ought to be blocked. v ¬ p ′ ∧ v ¬ q ′
T he S tandard P uzzle C onstructing the model E xplaining the semantics Q uestion dependency T he S tory D eontic situation : miners ’ location unknown Dead Shafts Blocked None Some All All Some illclogo . pdf None A nswer to the deontic question in this epistemic state : Neither shaft ought to be blocked. v ¬ p ′ ∧ v ¬ q ′ (5)
T he S tandard P uzzle C onstructing the model E xplaining the semantics Q uestion dependency T he S tory D eontic situation : miners ’ location known Rescuers learn that the miners are in shaft A. Dead Shafts Blocked None Some All illclogo . pdf A nswer to the deontic question in this epistemic state : v p ′ (6) Shaft A ought to be blocked.
T he S tandard P uzzle C onstructing the model E xplaining the semantics Q uestion dependency T he S tory D eontic question depends on the epistemic one D eontic question (7) Ought shaft A be blocked, or shaft B, or neither? ?( v p ′ ∨ v q ′ ∨ ( v ¬ p ′ ∧ v ¬ q ′ )) E pistemic question (8) Is it the case that the miners might be in shaft A and ?( � p ∧ � q ) they might be in B ? illclogo . pdf a. Yes, they might be in shaft A and they might be in shaft B. � p ∧ � q b. No, they must be in shaft A. � p c. No, they must be in shaft B. � q
T he S tandard P uzzle C onstructing the model E xplaining the semantics Q uestion dependency T he S tory D eontic question depends on the epistemic one D eontic question (7) Ought shaft A be blocked, or shaft B, or neither? ?( v p ′ ∨ v q ′ ∨ ( v ¬ p ′ ∧ v ¬ q ′ )) E pistemic question (8) Is it the case that the miners might be in shaft A and ?( � p ∧ � q ) they might be in B ? illclogo . pdf a. Yes, they might be in shaft A and they might be in shaft B. � p ∧ � q b. No, they must be in shaft A. � p c. No, they must be in shaft B. � q
T he S tandard P uzzle C onstructing the model E xplaining the semantics Q uestion dependency T he S tory D eontic question depends on the epistemic one I f the epistemic question is resolved , the deontic one is too . If the miners might be in shaft A and they might be in shaft B , then neither shaft ought to be blocked. ( � p ∧ � q ) → ( v ¬ p ′ ∧ v ¬ q ′ ) If the miners must be shaft A , shaft A ought to be � p → v p ′ blocked. If the miners must be shaft B , shaft B ought to be illclogo . pdf � q → v q ′ blocked. C onclusion : Full picture of the deontic information should distinguish epistemic possibilities.
T he S tandard P uzzle C onstructing the model E xplaining the semantics Q uestion dependency T he S tory D eontic question depends on the epistemic one I f the epistemic question is resolved , the deontic one is too . If the miners might be in shaft A and they might be in shaft B , then neither shaft ought to be blocked. ( � p ∧ � q ) → ( v ¬ p ′ ∧ v ¬ q ′ ) If the miners must be shaft A , shaft A ought to be � p → v p ′ blocked. If the miners must be shaft B , shaft B ought to be illclogo . pdf � q → v q ′ blocked. C onclusion : Full picture of the deontic information should distinguish epistemic possibilities.
T he S tandard P uzzle C onstructing the model E xplaining the semantics Q uestion dependency T he S tory P icture of the question dependency Shafts Blocked Shafts Blocked illclogo . pdf A nswer doesn ’ t depend only on the ontic information (9) If the miners are in shaft A, shaft A ought to be blocked. p → v p ′ a a See von Fintel 2012 for discussion.
T he S tandard P uzzle C onstructing the model E xplaining the semantics Q uestion dependency T he S tory P icture of the question dependency Shafts Blocked Shafts Blocked illclogo . pdf A nswer doesn ’ t depend only on the ontic information (9) If the miners are in shaft A, shaft A ought to be blocked. p → v p ′ a a See von Fintel 2012 for discussion.
T he S tandard P uzzle C onstructing the model E xplaining the semantics Q uestion dependency T he S tory E pistemic versus ontic A nswer doesn ’ t depend only on the ontic information (10) If the miners are in shaft A, shaft A ought to be blocked. p → v p ′ C onclusion : illclogo . pdf The antecedent is taken to be the prejacent of a covert epistemic necessity operator, that contextually relates to the information of the person amenable to the obligation.
T he S tandard P uzzle C onstructing the model E xplaining the semantics Q uestion dependency B uilding blocks D eontic information models 1 I ngredients of a deontic information model M worlds is a non empty set states powerset of the set of worlds facts maps atoms to { 0 , 1 } in each world assigns an (information) state to each world e-state v-state assign a (violation) state to each world illclogo . pdf e-state (w) the information state in w of a contextually given agent. v-state (w) the set of worlds where a rule that holds in w is violated. 1 We’re drawing on Aher and Groenendijk 2015 and Ciardelli and Roelofsen 2015.
T he S tandard P uzzle C onstructing the model E xplaining the semantics Q uestion dependency B uilding blocks S tandard constraints on e - state : ∀ w , v ∈ worlds : if v ∈ e-state ( w ) , then e-state ( v ) = e-state ( w ) (Introspection) ∀ w ∈ worlds : w ∈ e-state ( w ) . (Trust) Introspection and Trust guarantee that e-state induces a partition on worlds . C onstraint on v - state : illclogo . pdf ∀ w , v ∈ worlds : v-state ( w ) = v-state ( v ) (Indisputability) Indisputability guarantees that v-state rigidly characterizes a set of worlds: bad = { v ∈ worlds | ∃ w : v ∈ v-state ( w ) }
T he S tandard P uzzle C onstructing the model E xplaining the semantics Q uestion dependency B uilding blocks S tandard constraints on e - state : ∀ w , v ∈ worlds : if v ∈ e-state ( w ) , then e-state ( v ) = e-state ( w ) (Introspection) ∀ w ∈ worlds : w ∈ e-state ( w ) . (Trust) Introspection and Trust guarantee that e-state induces a partition on worlds . C onstraint on v - state : illclogo . pdf ∀ w , v ∈ worlds : v-state ( w ) = v-state ( v ) (Indisputability) Indisputability guarantees that v-state rigidly characterizes a set of worlds: bad = { v ∈ worlds | ∃ w : v ∈ v-state ( w ) }
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